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Notes on Integrable Motion of Two Interacting Curves and Two-layer Generalized Heisenberg Ferromagnet Equations

Exactly Solvable and Integrable Systems 2018-11-30 v1
Authors: Zhaidary Myrzakulova , Akbota Myrzakul , Gulgassyl Nugmanova , Ratbay Myrzakulov
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Abstract

In the present paper, we study the integrable 2-layer generalized Heisenberg ferromagnet equation (HFE). The relation between this generalized HFE and differential geometry of curves is established. Using this relation we found the geometrical equivalent counterpart of the 2-layer spin system which is the 2-component KdV equation. Finally, the gauge equivalence between these equations is established.

Keywords

integrable systems heisenberg ferromagnet equation differential geometry curve motion kdv equation gauge equivalence

Cite

@article{arxiv.1811.12216,
  title  = {Notes on Integrable Motion of Two Interacting Curves and Two-layer Generalized Heisenberg Ferromagnet Equations},
  author = {Zhaidary Myrzakulova and Akbota Myrzakul and Gulgassyl Nugmanova and Ratbay Myrzakulov},
  journal= {arXiv preprint arXiv:1811.12216},
  year   = {2018}
}

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12 pages

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